GIY Ireland, Together We Grow

We have a bed of asparagus now in it’s third year. We have not cut any, looking forward to next year, however this year the plants went mad with foliage over four feet high and still no sign of dying back . We need to earth up these plants but all the information says to wait until the foliage has died back. Can we cut the plants down or just mulch and earth up with the foliage still in place.
Thanks.